Question

You are creating a portfolio of two stocks. The first one has a standard deviation of 29% and the second one has a standard deviation of 39%. The correlation coefficient between the returns of the two is 0.4. You will invest 47% of the portfolio in the first stock and the rest in the second stock. What will be the standard deviation of this portfolio's returns? Answer in percent, rounded to two decimal places (e.g., 4.32%=4.32).

Answer 1

wiai+wia+2w, W2 Pi 2 C1 G2 oportfolio Where: Proportion of the portfolio invested in Asset 1 Proportion of the portfolio invested in Asset 2 Asset 1 standard deviation of returns Asset 2 standard deviation of returns Correlation coefficient between the returns of Asset 1 and Asset 2 P12

w1 = 47%, w2 = 1 - 47% = 53%

$\sigma = \sqrt{(0.47 * 0.29)^2 +(0.53 * 0.39) * (2 * 0.47 * 0.29 * 0.53 * 0.39 * 0.4)}$

$\sigma = \sqrt{0.018578 + 0.042725 + 0.022539}$

$\sigma = \sqrt{0.083841}$

Standard deviation = 28.96%